The past few months, I encountered one term again and again in the data science world: Markov Chain Monte Carlo. In my research lab, in podcasts, in articles, every time I heard the phrase I would nod and think that sounds pretty cool with only a vague idea of what anyone was talking about. Several times I tried to learn MCMC and Bayesian inference, but every time I started reading the books, I soon gave up. Exasperated, I turned to the best method to learn any new skill: apply it to a problem. Using some of my sleep data I had been meaning to explore and a hands-on application-based book (Bayesian Methods for Hackers, available free online), I finally learned Markov Chain Monte Carlo through a real-world project.

In real-world applications, it is conceivable that only positive and unlabeled (PU) data are available for training a classifier. For instance, in land-cover image classification, images of urban regions can be easily labeled, while images of non-urban regions are difficult to annotate due to high diversity of non-urban regions containing, e.g., forest, seas, grasses, and soil (Li et al., 2011). To cope with such situations, PU classification has been actively studied (Letouzey et al., 2000; Elkan and Noto, 2008; du Plessis et al., 2015), and the state-of-the-art method allows us to systematically train deep neural networks only from PU data (Kiryo et al., 2017). However, existing PU classification methods typically require an estimate of the class-prior probability, and their performance is sensitive to the quality of class-prior estimation (Kiryo et al., 2017). Although various class-prior estimation methods from PU data have been proposed so far (du Plessis and Sugiyama, 2014; Ramaswamy et al., 2016; Jain et al., 2016; du Plessis et al., 2017; Northcutt et al., 2017), accurate estimation of the class-prior is still highly challenging particularly for high-dimensional data.

We further assume that the space X is continuous. Such optimization problems are common in scientific and engineering fields. Examples include learning continuous valuation models (Eric, Freitas and Ghosh, 2008), automatic gait optimization for both quadrupedal and bipedal robots (Lizotte et al., 2007), choosing the optimal derivative of a molecule that best treats a disease (Negoescu, Frazier and Powell, 2011), tuning Hamiltonian based Monte Carlo Samplers (Wang, Mohamed and de Freitas, 2013), etc. A good survey of the problem in practical machine learning applications is presented in Snoek, Larochelle and Adams (2012). We were motivated to study this problem with the application of ranking multiple items on a webpage so as to optimize a diverse range of business metrics like user engagement and revenue from advertisements. In our example, the function f(x) is a utility function composed of various business metrics and x are parameters or knobs that control the relative frequency of different types of items we show on the webpage.

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian approximation computed using a receding history of iterates and gradients. It is the Markov chain nature of the classic stochastic gradient algorithm that enables this development. The construction offers a mechanism for stochastic line search adapting the step length. We numerically evaluate and compare against current state-of-the-art with encouraging performance on real-world benchmark problems where the number of observations and unknowns is in the order of millions.

A key phase in the bridge design process is the selection of the structural system. Due to budget and time constraints, engineers typically rely on engineering judgment and prior experience when selecting a structural system, often considering a limited range of design alternatives. The objective of this study was to explore the suitability of supervised machine learning as a preliminary design aid that provides guidance to engineers with regards to the statistically optimal bridge type to choose, ultimately improving the likelihood of optimized design, design standardization, and reduced maintenance costs. In order to devise this supervised learning system, data for over 600,000 bridges from the National Bridge Inventory database were analyzed. Key attributes for determining the bridge structure type were identified through three feature selection techniques. Potentially useful attributes like seismic intensity and historic data on the cost of materials (steel and concrete) were then added from the US Geological Survey (USGS) database and Engineering News Record. Decision tree, Bayes network and Support Vector Machines were used for predicting the bridge design type. Due to state-to-state variations in material availability, material costs, and design codes, supervised learning models based on the complete data set did not yield favorable results. Supervised learning models were then trained and tested using 10-fold cross validation on data for each state. Inclusion of seismic data improved the model performance noticeably. The data was then resampled to reduce the bias of the models towards more common design types, and the supervised learning models thus constructed showed further improvements in performance. The average recall and precision for the state models was 88.6% and 88.0% using Decision Trees, 84.0% and 83.7% using Bayesian Networks, and 80.8% and 75.6% using SVM.

The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation data. In particular, we cast the coarse-graining process under a probabilistic state-space model where the transition law dic- tates the evolution of the CG state variables and the emission law the coarse-to-fine map. The directed probabilistic graphical model implied, suggests that given values for the fine- grained (FG) variables, probabilistic inference tools must be employed to identify the cor- responding values for the CG states and to that end, we employ Stochastic Variational In- ference. We advocate a sparse Bayesian learning perspective which avoids overfitting and reveals the most salient features in the CG evolution law. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the pre- dictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system. We demonstrate the efficacy of the proposed frame- work in high-dimensional systems of random walkers.

Bayesian learning has been recently considered as an effective means of accounting for uncertainty in trained deep network parameters. This is of crucial importance when dealing with small or sparse training datasets. On the other hand, shallow models that compute weighted sums of their inputs, after passing them through a bank of arbitrary randomized nonlinearities, have been recently shown to enjoy good test error bounds that depend on the number of nonlinearities. Inspired from these advances, in this paper we examine novel deep network architectures, where each layer comprises a bank of arbitrary nonlinearities, linearly combined using multiple alternative sets of weights. We effect model training by means of approximate inference based on a t-divergence measure; this generalizes the Kullback-Leibler divergence in the context of the t-exponential family of distributions. We adopt the t-exponential family since it can more flexibly accommodate real-world data, that entail outliers and distributions with fat tails, compared to conventional Gaussian model assumptions. We extensively evaluate our approach using several challenging benchmarks, and provide comparative results to related state-of-the-art techniques.

Inference amortization methods allow the sharing of statistical strength across related observations when learning to perform posterior inference. Generally this requires the inversion of the dependency structure in the generative model, as the modeller must design and learn a distribution to approximate the posterior. Previous methods invert the dependency structure in a heuristic way and fail to capture the dependencies in the model, therefore limiting the performance of the eventual inference algorithm. We introduce an algorithm for faithfully and minimally inverting the graphical model structure of any generative model. Such an inversion has two crucial properties: a) it does not encode any independence assertions absent from the model, and b) for a given inversion, it encodes as many true independence assertions as possible. Our algorithm works by simulating variable elimination on the generative model to reparametrize the distribution. We show with experiments how such minimal inversions can assist in performing better inference.

As the term "machine learning" has heated up, interest in "robotics" (as expressed in Google Trends) has not altered much over the last three years. So how much of a place is there for machine learning in robotics? While only a portion of recent developments in robotics can be credited to developments and uses of machine learning, I've aimed to collect some of the more prominent applications together in this article, along with links and references. Before I delve into machine learning in robotics, go ahead and define "robot". Though at first this might seem simple, it's no easy task to come to an agreement on just what a robot is and what it is not, even amongst roboticists.

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be investigated via the spectrum of the Hessian of the empirical loss function. Network data can be understood via the eigenstructure of a graph Laplacian matrix using spectral graph theory. Quantum simulations and other many-body problems are often characterized via the eigenvalues of the solution space, as are various dynamic systems. However, naive eigenvalue estimation is computationally expensive even when the matrix can be represented; in many of these situations the matrix is so large as to only be available implicitly via products with vectors. Even worse, one may only have noisy estimates of such matrix vector products. In this work, we combine several different techniques for randomized estimation and show that it is possible to construct unbiased estimators to answer a broad class of questions about the spectra of such implicit matrices, even in the presence of noise. We validate these methods on large-scale problems in which graph theory and random matrix theory provide ground truth.